//
// Description : Array and textureless GLSL 2D/3D/4D simplex
//               noise functions.
//      Author : Ian McEwan, Ashima Arts.
//  Maintainer : stegu
//     Lastmod : 20110822 (ijm)
//     License : Copyright (C) 2011 Ashima Arts. All rights reserved.
//               Distributed under the MIT License. See LICENSE file.
//               https://github.com/ashima/webgl-noise
//               https://github.com/stegu/webgl-noise
//

vec4 grad4( float j, vec4 ip ) {

    const vec4 ones = vec4( 1.0, 1.0, 1.0, -1.0 );
    vec4 p, s;

    p.xyz = floor( fract( vec3( j ) * ip.xyz ) * 7.0 ) * ip.z - 1.0;
    p.w = 1.5 - dot( abs( p.xyz ), ones.xyz );
    s = vec4( lessThan( p, vec4( 0.0 ) ) );
    p.xyz = p.xyz + ( s.xyz * 2.0 - 1.0 ) * s.www;

    return p;

}

// (sqrt(5) - 1)/4 = F4, used once below
#define F4 0.309016994374947451

float simplex(vec4 v) {

    const vec4 C = vec4( 0.138196601125011,  // (5 - sqrt(5))/20  G4
                        0.276393202250021,  // 2 * G4
                        0.414589803375032,  // 3 * G4
                        -0.447213595499958); // -1 + 4 * G4

    // First corner
    vec4 i  = floor( v + dot( v, vec4( F4 ) ) );
    vec4 x0 = v - i + dot( i, C.xxxx );

    // Other corners

    // Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI)
    vec4 i0;
    vec3 isX = step( x0.yzw, x0.xxx );
    vec3 isYZ = step( x0.zww, x0.yyz );
    i0.x = isX.x + isX.y + isX.z;
    i0.yzw = 1.0 - isX;
    i0.y += isYZ.x + isYZ.y;
    i0.zw += 1.0 - isYZ.xy;
    i0.z += isYZ.z;
    i0.w += 1.0 - isYZ.z;

    vec4 i3 = clamp( i0, 0.0, 1.0 );
    vec4 i2 = clamp( i0 - 1.0, 0.0, 1.0 );
    vec4 i1 = clamp( i0 - 2.0, 0.0, 1.0 );

    vec4 x1 = x0 - i1 + C.xxxx;
    vec4 x2 = x0 - i2 + C.yyyy;
    vec4 x3 = x0 - i3 + C.zzzz;
    vec4 x4 = x0 + C.wwww;

    // Permutations
    i = mod289( i );
    float j0 = permute( permute( permute( permute( i.w ) + i.z ) + i.y ) + i.x );
    vec4 j1 = permute( permute( permute( permute (
                i.w + vec4(i1.w, i2.w, i3.w, 1.0 ))
            + i.z + vec4(i1.z, i2.z, i3.z, 1.0 ))
            + i.y + vec4(i1.y, i2.y, i3.y, 1.0 ))
            + i.x + vec4(i1.x, i2.x, i3.x, 1.0 ));

    // Gradients: 7x7x6 points over a cube, mapped onto a 4-cross polytope
    // 7*7*6 = 294, which is close to the ring size 17*17 = 289.
    vec4 ip = vec4( 1.0 / 294.0, 1.0 / 49.0, 1.0 / 7.0, 0.0 );

    vec4 p0 = grad4(j0,   ip);
    vec4 p1 = grad4(j1.x, ip);
    vec4 p2 = grad4(j1.y, ip);
    vec4 p3 = grad4(j1.z, ip);
    vec4 p4 = grad4(j1.w, ip);

    // Normalise gradients
    vec4 norm = taylorInvSqrt( vec4( dot( p0, p0 ), dot( p1, p1 ), dot( p2, p2 ), dot( p3, p3 ) ) );
    p0 *= norm.x;
    p1 *= norm.y;
    p2 *= norm.z;
    p3 *= norm.w;
    p4 *= taylorInvSqrt( dot( p4, p4 ) );

    // Mix contributions from the five corners
    vec3 m0 = max( 0.6 - vec3( dot( x0, x0 ), dot( x1, x1 ), dot( x2, x2 ) ), 0.0 );
    vec2 m1 = max( 0.6 - vec2( dot( x3, x3 ), dot( x4, x4 ) ), 0.0 );
    m0 = m0 * m0;
    m1 = m1 * m1;
    return 49.0 * ( dot(m0*m0, vec3( dot( p0, x0 ), dot( p1, x1 ), dot( p2, x2 )))
                + dot(m1*m1, vec2( dot( p3, x3 ), dot( p4, x4 ) ) ) ) ;

}
